Ultrasonic casing and cement evaluation method using a ray tracing model

ABSTRACT

Systems, methods, and software for determining a thickness of a well casing are described. In some aspects, the thickness of the well casing is determined based on results of comparing a measured waveform and model waveforms. The measured waveform and model waveforms are generated based on operating an acoustic transmitter and an acoustic receiver within a wellbore comprising the well casing.

BACKGROUND

This disclosure relates to measuring the thickness of a well casing of awell structure.

Cement evaluation techniques can be used to measure the thickness of awell casing installed inside of a well (e.g., oil well structures) usingacoustic waves. The accuracy of casing thickness measurement is not onlyimportant for correctly assessing casing damage, but also is critical toevaluating the quality of cement bonding between the casing and asurrounding formation. These assessments are essential to the safety andeconomy of oil field operations.

DESCRIPTION OF DRAWINGS

FIG. 1A is a diagram of an example well system.

FIG. 1B is a diagram of an example well system that includes a loggingtool in a wireline logging environment.

FIG. 1C is a diagram of an example well system that includes a loggingtool in a logging while drilling (LWD) environment.

FIG. 2 is a diagram of an example computing system.

FIG. 3 shows an example tool having a one-transducer pulse-echoconfiguration.

FIG. 4 shows an example tool having a two-transducer pitch-catchconfiguration.

FIG. 5 shows a typical waveform recorded by a pulse-echo configuration.

FIG. 6 shows an example of a plane wave model.

FIG. 7 shows an example of modeled and measured waves.

FIG. 8 shows an example of the cross-correlation as a function ofassumed casing thickness.

FIG. 9 is a flowchart showing an example technique for measuring thethickness of a well casing of a well structure.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

FIG. 1A is a diagram of an example well system 100 a. The example wellsystem 100 a includes a logging system 108 and a subterranean region 120beneath the ground surface 106. A well system can include additional ordifferent features that are not shown in FIG. 1A. For example, the wellsystem 100 a may include additional drilling system components, wirelinelogging system components, etc.

The subterranean region 120 can include all or part of one or moresubterranean formations or zones. The example subterranean region 120shown in FIG. 1A includes multiple subsurface layers 122 and a wellbore104 penetrated through the subsurface layers 122. The subsurface layers122 can include sedimentary layers, rock layers, sand layers, orcombinations of these other types of subsurface layers. One or more ofthe subsurface layers can contain fluids, such as brine, oil, gas, etc.Although the example wellbore 104 shown in FIG. 1A is a verticalwellbore, the logging system 108 can be implemented in other wellboreorientations. For example, the logging system 108 may be adapted forhorizontal wellbores, slant wellbores, curved wellbores, verticalwellbores, or combinations of these.

The example logging system 108 includes a logging tool 102, surfaceequipment 112, and a computing subsystem 110. In the example shown inFIG. 1A, the logging tool 102 is a downhole logging tool that operateswhile disposed in the wellbore 104. The example surface equipment 112shown in FIG. 1A operates at or above the surface 106, for example, nearthe well head 105, to control the logging tool 102 and possibly otherdownhole equipment or other components of the well system 100. Theexample computing subsystem 110 can receive and analyze logging datafrom the logging tool 102. A logging system can include additional ordifferent features, and the features of a logging system can be arrangedand operated as represented in FIG. 1A or in another manner.

In some instances, all or part of the computing subsystem 110 can beimplemented as a component of, or can be integrated with one or morecomponents of, the surface equipment 112, the logging tool 102, or both.In some cases, the computing subsystem 110 can be implemented as one ormore discrete computing system structures separate from the surfaceequipment 112 and the logging tool 102.

In some implementations, the computing subsystem 110 is embedded in thelogging tool 102, and the computing subsystem 110 and the logging tool102 can operate concurrently while disposed in the wellbore 104. Forexample, although the computing subsystem 110 is shown above the surface106 in the example shown in FIG. 1A, all or part of the computingsubsystem 110 may reside below the surface 106, for example, at or nearthe location of the logging tool 102.

The well system 100 a can include communication or telemetry equipmentthat allow communication among the computing subsystem 110, the loggingtool 102, and other components of the logging system 108. For example,the components of the logging system 108 can each include one or moretransceivers or similar apparatus for wired or wireless datacommunication among the various components. For example, the loggingsystem 108 can include systems and apparatus for wireline telemetry,wired pipe telemetry, mud pulse telemetry, acoustic telemetry,electromagnetic telemetry, or a combination of these other types oftelemetry. In some cases, the logging tool 102 receives commands, statussignals, or other types of information from the computing subsystem 110or another source. In some cases, the computing subsystem 110 receiveslogging data, status signals, or other types of information from thelogging tool 102 or another source.

Logging operations can be performed in connection with various types ofdownhole operations at various stages in the lifetime of a well system.Structural attributes and components of the surface equipment 112 andlogging tool 102 can be adapted for various types of logging operations.For example, logging may be performed during drilling operations, duringwireline logging operations, or in other contexts. As such, the surfaceequipment 112 and the logging tool 102 may include, or may operate inconnection with drilling equipment, wireline logging equipment, or otherequipment for other types of operations.

In some examples, logging operations are performed during wirelinelogging operations. FIG. 1B shows an example well system 100 b thatincludes the logging tool 102 in a wireline logging environment. In someexample wireline logging operations, the surface equipment 112 includesa platform above the surface 106 that is equipped with a derrick 132that supports a wireline cable 134 that extends into the wellbore 104.Wireline logging operations can be performed, for example, after adrilling string is removed from the wellbore 104, to allow the wirelinelogging tool 102 to be lowered by wireline or logging cable into thewellbore 104.

In some examples, logging operations are performed during drillingoperations. FIG. 1C shows an example well system 100 c that includes thelogging tool 102 in a logging while drilling (LWD) environment. Drillingis commonly carried out using a string of drill pipes connected togetherto form a drill string 140 that is lowered through a rotary table intothe wellbore 104. In some cases, a drilling rig 142 at the surface 106supports the drill string 140, as the drill string 140 is operated todrill a wellbore penetrating the subterranean region 120. The drillstring 140 may include, for example, a kelly, drill pipe, a bottom holeassembly, and other components. The bottom hole assembly on the drillstring may include drill collars, drill bits, the logging tool 102, andother components. The logging tools may include measuring while drilling(MWD) tools, LWD tools, and others.

As shown, for example, in FIG. 1B, the logging tool 102 can be suspendedin the wellbore 104 by a coiled tubing, wireline cable, or anotherstructure that connects the tool to a surface control unit or othercomponents of the surface equipment 112. In some exampleimplementations, the logging tool 102 is lowered to the bottom of aregion of interest and subsequently pulled upward (e.g., at asubstantially constant speed) through the region of interest. As shown,for example, in FIG. 1C, the logging tool 102 can be deployed in thewellbore 104 on jointed drill pipe, hard wired drill pipe, or otherdeployment hardware. In some example implementations, the logging tool102 collects data during drilling operations as it moves downwardthrough the region of interest during drilling operations. In someexample implementations, the logging tool 102 collects data while thedrilling string 140 is moving, for example, while it is being tripped inor tripped out of the wellbore 104.

In some example implementations, the logging tool 102 collects data atdiscrete logging points in the wellbore 104. For example, the loggingtool 102 can move upward or downward incrementally to each logging pointat a series of depths in the wellbore 104. At each logging point,instruments in the logging tool 102 perform measurements on thesubterranean region 120. The measurement data can be communicated to thecomputing subsystem 110 for storage, processing, and analysis. Such datamay be gathered and analyzed during drilling operations (e.g., duringlogging while drilling (LWD) operations), during wireline loggingoperations, or during other types of activities.

The computing subsystem 110 can receive and analyze the measurement datafrom the logging tool 102 to detect properties of various subsurfacelayers 122. For example, the computing subsystem 110 can identify thedensity, material content, or other properties of the subsurface layers122 based on the measurements acquired by the logging tool 102 in thewellbore 104.

FIG. 2 is a diagram of the example computing system 200. The examplecomputing system 200 can be used as the computing subsystem 110 of FIG.1A, 1B, or 1C, or the example computing system 200 can be used inanother manner. In some cases, the example computing system 200 canoperate in connection with a well system (e.g., the well systems 100 a,100 b, or 100 c shown in FIG. 1A, 1B, or 1C) and be located at or nearone or more wells of a well system or at a remote location. All or partof the computing system 200 may operate independent of a well system.

The example computing system 200 shown in FIG. 2 includes a memory 150,a processor 160, and input/output controllers 170 communicably coupledby a bus 165. The memory 150 can include, for example, a random accessmemory (RAM), a storage device (e.g., a writable read-only memory (ROM)or others), a hard disk, or another type of storage medium. Thecomputing subsystem 110 can be preprogrammed or it can be programmed(and reprogrammed) by loading a program from another source (e.g., froma CD-ROM, from another computer device through a data network, or inanother manner).

In some examples, the input/output controller 170 is coupled toinput/output devices (e.g., a monitor 175, a mouse, a keyboard, or otherinput/output devices) and to a communication link 180. The input/outputdevices receive and transmit data in analog or digital form overcommunication links such as a serial link, a wireless link (e.g.,infrared, radio frequency, or others), a parallel link, or another typeof link.

The communication link 180 can include any type of communicationchannel, connector, data communication network, or other link. Forexample, the communication link 180 can include a wireless or a wirednetwork, a Local Area Network (LAN), a Wide Area Network (WAN), aprivate network, a public network (such as the Internet), a WiFinetwork, a network that includes a satellite link, or another type ofdata communication network.

The memory 150 can store instructions (e.g., computer code) associatedwith an operating system, computer applications, and other resources.The memory 150 can also store application data and data objects that canbe interpreted by one or more applications or virtual machines runningon the computing system 200. As shown in FIG. 2, the example memory 150includes logging data 151, waveform data 152, other data 153, andapplications 154. The data and applications in the memory 150 can bestored in any suitable form or format.

The logging data 151 can include measurements and other data from alogging tool. In some cases, the logging data 151 include one or moremeasurements for each of multiple different logging points in awellbore. For example, the logging point associated with a givenmeasurement can be the location of the logging tool's reference pointwhen the given measurement was acquired. Each measurement can includedata obtained by one or more transmitter-receiver pairs operating at oneor more signal frequencies. Each measurement can include data obtainedby multiple transmitter-receiver pairs operating at one or moretransmitter-receiver spacings. The logging data 151 can includeinformation identifying a transmitter-receiver spacing associate witheach measurement.

The waveform data 152 can include measured waveforms and modelwaveforms. The measured waveforms can be used to determine the thicknessof a well casing. The model waveforms can correspond to differentassumed or estimated thicknesses of the well casing. The waveform data152 may include information associated with one or more logging points.

The other data 153 can include other information that is used by,generated by, or otherwise associated with the applications 154. Forexample, the other data 153 can include simulated data or otherinformation that can be used by an engine to produce the waveform data152 from the logging data 151.

The applications 154 can include software applications, scripts,programs, functions, executables, or other modules that are interpretedor executed by the processor 160. The applications 154 may includemachine-readable instructions for performing one or more of theoperations related to FIG. 9.

The applications 154 can obtain input data, such as logging data,simulation data, or other types of input data, from the memory 150, fromanother local source, or from one or more remote sources (e.g., via thecommunication link 180). The applications 154 can generate output dataand store the output data in the memory 150, in another local medium, orin one or more remote devices (e.g., by sending the output data via thecommunication link 180).

The processor 160 can execute instructions, for example, to generateoutput data based on data inputs. For example, the processor 160 can runthe applications 154 by executing or interpreting the software, scripts,programs, functions, executables, or other modules contained in theapplications 154. The processor 160 may perform one or more of theoperations related to FIG. 9. The input data received by the processor160 or the output data generated by the processor 160 can include any ofthe logging data 151, the waveform data 152, or the other data 153.

In some implementations, the logging tool 102 of FIGS. 1A, 1B, and 1Cincludes a casing inspection tool. Acoustic casing inspection tools andcement evaluation tools use transducers to emit acoustic waves into thewell casing, the cement behind the casing, and the formation. Theacoustic waves can be either body waves, such as compressional waves andshear waves, or surface waves. These acoustic waves travel inside thecasing, cement, and formation, and are reflected andrefracted/transmitted at each interface. The reflected andrefracted/transmitted waves carry information about the casing thicknessand cement bonding quality, and are recorded by either the originaltransducer or a second transducer for processing and interpretation(e.g., by an electronic processor of the tool). Measurements and/orprocessed data from the tool may be transmitted through a support cableto a surface control system, where they are reviewed by an operator. Insome implementations, either additionally or alternatively, measurementsmay be stored within the tool (e.g., in a data storage device) forfuture retrieval, processing, and/or review at the surface. In one ormore implementations, the measurements and/or processed data from thetool may be transmitted via other communication schemes (e.g. mud-pulsetelemetry, wired pipe, electromagnetic telemetry, acoustic telemetry,and/or other telemetry schemes) used downhole.

Acoustic casing inspection tools may be of various configurations.Example configurations are shown in FIGS. 3 and 4. A casing inspectiontool includes one or more transducers to direct an acoustic signaltowards a well casing and detect an acoustic signal returning from thewell casing. The transducers may be used as high amplitude transmittersto generate and direct acoustic energy towards the casing, and to detectenergy that is reflected by the casing and other surrounding media.Based on this reflected energy, the tool determines a thickness of thecasing (e.g., using an electronic processor of the tool to process thedetected energy).

FIG. 3 depicts an implementation of a casing inspection tool having aone-transducer pulse-echo configuration 300. The transducer 302 includesan acoustic transmitter and an acoustic receiver. Acoustic energy 304generated by the transducer 302 reflects from the interfaces of the wellcasing 306, and may reflect multiple times inside the casing 306, asshown by wave reverberation 308. Returning energy 310 is detected by thetransducer 302.

FIG. 4 depicts an implementation of a casing inspection tool having atwo-transducer pitch-catch configuration 400. The transducers include anacoustic transmitter 402 and an acoustic receiver 404. Acoustic energy405 generated by the transducer 402 reflects from the interfaces of thewell casing 406, and may reflect multiple times inside the casing 406,as shown by wave reverberation 408. Returning energy 410 is detected bythe receiver 404.

The thickness of the casing may be determined using the frequencycontent of the recorded waveforms. FIG. 5 illustrates a typical waveform500 recorded by a pulse-echo configuration, e.g., the pulse-echoconfiguration 300 of FIG. 3. The reverberation part of the waveform(within the time window T_(win)) comes from the waves being reflectedmultiple times inside the casing. The peak frequency of the casingreverberations is related to the casing thickness in the way that thecasing thickness is equal to one half (or any integer multiple of onehalf) of the wavelength of the wave oscillating at this peak frequency.Therefore, the casing thickness may be calculated by measuring the peakfrequency. However, the accuracy of the frequency measurement may belimited by many factors, such as the recording length of the waveform,the resolution of frequency, the transducer's firing frequency, andother factors. These factors may affect the accuracy of the casingthickness measurement. For example, for thick casings, the peakfrequency may become very low. Low frequency acoustic waves have a longwavelength, so a long distance is needed between the transducer and thecasing wall. However, in a cased borehole, this distance is limited bythe casing diameter. For small diameters the transducer-casing distancewill be small. Therefore, there will be less time to record the firstreflection and the following reverberations before the second reflectionarrives.

The correlation between the measured waveform and a model waveform maybe used to improve the accuracy of the thickness estimate of the wellcasing, and to reduce or eliminate the necessity of using low frequencyacoustic waves for thick casings. This correlation determination mayprovide an accurate casing thickness estimate, as the relative timedelay of each reverberation between the two interfaces of the casing issolely determined by the casing thickness, and is mostly independent ofthe impedance of the cement behind the casing. In addition, inapplications related to oil field construction and exploration, a wellcasing may be made of steel, which has higher acoustic impedance thanboth the borehole fluid and the cement.

The accuracy of thickness measurement may be essential for furtherevaluation of cement bonding behind the casing, which is critical forthe safety and economy of oil field operation. Conventional technologiesfor cement bonding evaluation are primarily designed for casings thinnerthan 1 inch. However, in oil fields where tectonic movements are active,thick casings are installed in the oil wells, often in excess of 1 inch.The correlation between the measured waveform and a model waveform canbe used to evaluate casings thicker than 1 inch.

This correlation method uses the same signal pulse in the model as theone used by the measurement. This may be achieved in various ways. Insome implementations, the first reflection (defined by T_(off) in FIG.5) from the casing's inner wall is used as a reference to calculate theentire waveform. In some implementations, the pre-measurement reflectionis used as the reference. As mentioned above, the casing thicknessestimate is largely independent of the impedance values of both innerfluid and the cement, which are assumed to be less than the impedance ofthe steel casing.

Several model waveforms may be calculated for many assumed or estimatedcasing thicknesses. Model waveforms may be calculated in various ways.For instance, in some implementations, model waveforms are calculatedaccording to a plane wave model 600, as shown in FIG. 6. In the planewave model 600, the casing 602 is simplified as a flat plate. Acousticwaves 604 generated by a transducer 606 reflects from the surfaces ofthe well casing 602, and may reflect multiple times inside the casing602, as shown by wave reverberation 608. Returning waves 610 aredetected by the transducer 606. The waves are all assumed to be planewaves. The waves are incident perpendicularly to the surfaces of thecasing 602.

In some implementations, model waveforms may be calculated using moreadvanced models that may include the effects of casing curvature, thetransducer's radiation pattern, etc. For example, model waveforms may becalculated using a ray tracing model that accounts for beam spreading ofthe transducer and the curvature of the casing. In some implementations,a theoretical model of ultrasonic propagation is built using aparticular tool configuration (for example, a pulse-echo configuration)with an assumed cement bonding impedance and casing thickness. Theacoustic waves emitted from the transmitter are decomposed into manyrays traveling to different directions. These rays are represented asplane waves. The magnitude of each ray is weighted according to itsdirection by the transducer's radiation pattern so that the beamspreading effect is taken into account.

For example, when a ray is in a medium corresponding to the boreholefluid, it is a pure compressional wave. When a ray reaches the innerwall of the casing, it is reflected and refracted according to theinterface's boundary condition. The refracted waves will have bothcompressional and shear waves. Both compressional and shear waves can beconverted into each other at either of the two interfaces of the casing.In some implementations, this wave may be converted at the interfacesbetween a compressional wave and a shear wave, and vice versa. In someimplementations, the model may be simplified further by including onlycompressional waves in the analysis.

When the refracted waves travel inside the casing, they are reflectedand refracted multiple times by both inner and outer walls of thecasing. Some of the acoustic energy leaks into the cement and the rockformation around the borehole. Some acoustic waves are reflected backinto the borehole fluid and recorded by the acoustic transducer. Thesereflected waves carry the information about the casing thickness and theacoustic impedance behind the casing. In one or more implementations,the reflections and refractions of each ray are traced (both the anglesand magnitudes) at the curved casing walls. The incident angle, thereflection angles, and the refraction angles of each ray are calculatedaccording to its travel direction and the effect of the casingcurvature. By adding all the waves coming into the transducer, the modelwaveform can be calculated. Model waveforms calculated based on traveldirection and casing curvature may be more accurate than model waveformscreated using normal-incident plane-wave theory.

FIG. 7 shows a graph 700 of examples of a model waveform and a measuredwaveform. The correlation between the measured and model waveformswithin the reverberation window for each assumed thickness may becalculated. The thickness corresponding to the maximum value of thecorrelation is the estimated casing thickness.

In some implementations, the correlation of the model and measuredwaveforms is calculated by determining the cross-correlation of themodel and measured waveforms. FIG. 8 shows a graph 800 of an example ofthe cross-correlation as a function of assumed casing thickness. Thetrue (i.e., measured) casing thickness is 1.2 inches in this example,and the cross-correlation shows a peak at that value in the plot aswell. In some implementations, the correlation of the model and measuredwaveforms is calculated by finding the difference of the two as afunction of assumed casing thickness. The thickness corresponding to theminimum difference is the estimated casing thickness.

FIG. 9 is a flowchart showing an example process 900 for determining athickness of a well casing. Some or all of the operations in the process900 can be implemented by one or more computing devices. For example,the process 900 can be implemented by the computing subsystem 110 inFIG. 1A, the computing system 200 in FIG. 2, or by another type ofsystem.

Some or all of the operations in the process 900 can be implemented byone or more computing devices that are embedded with, or otherwiseoperated in connection with, a logging tool. For example, the process900 can be implemented in connection with the logging tool 102 in FIG.1A, the casing evaluation tools in FIGS. 3 and 4, or another type oftool. The casing evaluation tool may include an acoustic transmitter totransmit acoustic energy to a well casing. The casing evaluation toolmay include an acoustic receiver to detect acoustic energy returning viathe well casing. The transmitter and receiver can be operated within awellbore that includes a well casing.

In some implementations, the process 900 may include additional, fewer,or different operations performed in the order shown in FIG. 9, or in adifferent order. Moreover, one or more of the individual operations orsubsets of the operations in the process 900 can be performed inisolation, or as part of another process. Output data generated by theprocess 900, including output data generated by intermediate operations,can include stored, displayed, printed, transmitted, communicated orprocessed information.

In some implementations, some or all of the operations in the process900 are executed in real time during a drilling operation or anothertype of operation performed in a well system. An operation can beperformed in real time, for example, by performing the operation inresponse to receiving data (e.g., from a sensor or monitoring system)without substantial delay. An operation can be performed in real time,for example, by performing the operation while monitoring for additionaldata. Some real time operations can receive an input and produce anoutput during drilling operations; in some instances, the output is madeavailable within a time frame that allows an operator (e.g., a human ormachine operator) to respond to the output, for example, by modifyingthe drilling operation.

In some implementations, a casing evaluation tool can be placed in awellbore defined in a subterranean region that includes multiplesubsurface layers. For example, the casing evaluation tool can be thelogging tool 102 shown in FIG. 1A. The casing evaluation tool can betransported by a drilling assembly, by a wireline logging assembly, orother hardware. The casing evaluation tool can be operated at multipletool depths in the wellbore, and each tool depth can represent adifferent logging point. The process 900 can be executed based on datafor a single logging point or multiple logging points.

At 902, a measured waveform associated with an acoustic signal returnedvia a well casing based on operating an acoustic transmitter and anacoustic receiver within a wellbore that includes the well casing isaccessed.

At 904, model waveforms for assumed thicknesses are generated based on areflection of the acoustic signal, a radiation pattern of the acoustictransmitter, a curvature of the well casing, or a combination. Eachmodel waveform corresponds to a different assumed or estimated thicknessof the well casing. In some implementations, the model waveforms maycorrespond to an assumed well casing thickness greater than 1 inch.

At 906, the measured waveform is compared to the model waveforms.Comparing the measured waveform to the model waveforms may includedetermining correlations between a portion of the measured waveform anda portion of each of the model waveforms. The portion of the measuredwaveform and the portion of each of the model waveforms may correspondto a reverberation window of the measured waveform. In someimplementations, determining correlations may include determiningcross-correlations between the measured waveform and the modelwaveforms. In some implementations, determining correlations may includedetermining differences between the measured waveform and the modelwaveforms.

At 908, a thickness of the well casing is determined based on results ofcomparing the measured waveform and the plurality of model waveforms. Insome implementations, the thickness corresponding to the maximum valueof the correlation is the estimated casing thickness. In implementationswhere differences between the measured waveform and the model waveformsare determined, the thickness of the well casing may be determined bydetermining a thickness corresponding to a model waveform thatcorresponds to a minimum difference between the measured waveform andthe model waveforms.

The techniques described above can be implemented in digital electroniccircuitry, or in computer software, firmware, or hardware, including thestructures disclosed in this specification and their structuralequivalents, or in combinations of one or more of them. For example, anelectronic processor may be used to control acoustic transmitters andreceivers (e.g., by sending electronic command signals) in order todirect an acoustic signal towards a casing and detect an acoustic signalreturning from the pipe. In another example, the electronic processormay be used to analyze and process data, for instance to determine athickness of the casing using one or more of the techniques describedabove.

The term “electronic processor” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, a system on a chip, or multipleones, or combinations, of the foregoing. The apparatus can includespecial purpose logic circuitry, e.g., an FPGA (field programmable gatearray) or an ASIC (application specific integrated circuit). Theapparatus can also include, in addition to hardware, code that createsan execution environment for the computer program in question, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, a cross-platform runtimeenvironment, a virtual machine, or a combination of one or more of them.The apparatus and execution environment can realize various differentcomputing model infrastructures, such as web services, distributedcomputing and grid computing infrastructures.

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for performing actions in accordance with instructions andone or more memory devices for storing instructions and data. Generally,a computer will also include, or be operatively coupled to receive datafrom or transfer data to, or both, one or more mass storage devices forstoring data, e.g., magnetic, magneto optical disks, or optical disks.However, a computer need not have such devices. Moreover, a computer canbe embedded in another device, e.g., a mobile telephone, a personaldigital assistant (PDA), a mobile audio or video player, a game console,a Global Positioning System (GPS) receiver, or a portable storage device(e.g., a universal serial bus (USB) flash drive), to name just a few.Devices suitable for storing computer program instructions and datainclude all forms of non-volatile memory, media and memory devices,including by way of example semiconductor memory devices, e.g., EPROM,EEPROM, and flash memory devices; magnetic disks, e.g., internal harddisks or removable disks; magneto optical disks; and CD ROM and DVD-ROMdisks. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages. A computer program may, but need not, correspondto a file in a file system. A program can be stored in a portion of afile that holds other programs or data (e.g., one or more scripts storedin a markup language document), in a single file dedicated to theprogram in question, or in multiple coordinated files (e.g., files thatstore one or more modules, sub programs, or portions of code). Acomputer program can be deployed to be executed on one computer or onmultiple computers that are located at one site or distributed acrossmultiple sites and interconnected by a communication network.

To provide for interaction with a user, operations can be implemented ona computer having a display device (e.g., a monitor, or another type ofdisplay device) for displaying information to the user and a keyboardand a pointing device (e.g., a mouse, a trackball, a tablet, a touchsensitive screen, or another type of pointing device) by which the usercan provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback, e.g., visualfeedback, auditory feedback, or tactile feedback; and input from theuser can be received in any form, including acoustic, speech, or tactileinput. In addition, a computer can interact with a user by sendingdocuments to and receiving documents from a device that is used by theuser; for example, by sending web pages to a web browser on a user'sclient device in response to requests received from the web browser.

A client and server are generally remote from each other and typicallyinteract through a communication network. Examples of communicationnetworks include a local area network (“LAN”) and a wide area network(“WAN”), an inter-network (e.g., the Internet), a network comprising asatellite link, and peer-to-peer networks (e.g., ad hoc peer-to-peernetworks). The relationship of client and server arises by virtue ofcomputer programs running on the respective computers and having aclient-server relationship to each other.

While this specification contains many details, these should not beconstrued as limitations on the scope of what may be claimed, but ratheras descriptions of features specific to particular examples. Certainfeatures that are described in this specification in the context ofseparate implementations can also be combined. Conversely, variousfeatures that are described in the context of a single implementationcan also be implemented in multiple implementations separately or in anysuitable subcombination.

A number of implementations have been described. Nevertheless, it willbe understood that other implementations are also possible. For example,the method may include fewer steps than those illustrated or more stepsthan those illustrated. In addition the steps may be performed in therespective order or in different orders than illustrated.

In one general aspect, a thickness of the well casing is determinedbased on results of comparing the measured waveform and the plurality ofmodel waveforms.

In some aspects, a measured waveform associated with an acoustic signalreturned via a well casing is accessed based on operating an acoustictransmitter and an acoustic receiver within a wellbore comprising thewell casing. The measured waveform is compared to a plurality of modelwaveforms. Each of the plurality of model waveforms corresponds to adifferent thickness of the well casing. A thickness of the well casingis determined based on results of comparing the measured waveform andthe plurality of model waveforms.

Implementations of these and other aspects may include one or more ofthe following features. Comparing the measured waveform to the pluralityof model waveforms includes determining correlations between at least aportion of the measured waveform and at least a portion of each of theplurality of model waveforms. At least a portion of the measuredwaveform corresponds to a reverberation window of the measured waveform.Determining the correlations between the at least a portion of themeasured waveform and the at least a portion of each of the plurality ofmodel waveforms includes determining cross-correlations between the atleast a portion of the measured waveform and the at least a portion ofeach of the plurality of model waveforms. Determining the correlationsbetween the at least a portion of the measured waveform and the at leasta portion of each of the plurality of model waveforms includesdetermining differences between the at least a portion of the measuredwaveform and the at least a portion of each of the plurality of modelwaveforms. Determining the thickness of the well casing includesdetermining a thickness corresponding to a model waveform of theplurality of model waveforms corresponding to a minimum difference ofthe determined differences.

Additionally or alternatively, implementations of these and otheraspects may include one or more of the following features. The pluralityof model waveforms for a plurality of assumed thicknesses are generatedbased on one or more of (i) a reflection of the acoustic signal, (ii) aradiation pattern of the acoustic transmitter, and (iii) a curvature ofthe well casing. Determining the thickness of the well casing includesdetermining the thickness of the well casing in real time duringdrilling operations or wireline logging operations.

In some aspects, a system includes an acoustic transmitter-receiver pairto be disposed within an interior portion of a well casing, and acomputing system coupled with the acoustic transmitter-receiver pair.The computing system is configured to access a measured waveformassociated with an acoustic signal returned via the well casing based onoperating an acoustic transmitter and an acoustic receiver within awellbore comprising the well casing and compare the measured waveform toa plurality of model waveforms. Each of the plurality of model waveformscorresponds to a different thickness of the well casing. The computingsystem is configured to determine a thickness of the well casing basedon results of comparing the measured waveform and the plurality of modelwaveforms.

Implementations of these and other aspects may include one or more ofthe following features. The computing system is configured to determinecorrelations between at least a portion of the measured waveform and atleast a portion of each of the plurality of model waveforms. At least aportion of the measured waveform corresponds to a reverberation windowof the measured waveform. The computing system is configured todetermine cross-correlations between the at least a portion of themeasured waveform and the at least a portion of each of the plurality ofmodel waveforms. The computing system is configured to determinedifferences between the at least a portion of the measured waveform andthe at least a portion of each of the plurality of model waveforms, andto determine the thickness of the well casing comprises the computingsystem to determine a thickness corresponding to a model waveform of theplurality of model waveforms corresponding to a minimum difference ofthe determined differences.

Additionally or alternatively, implementations of these and otheraspects may include one or more of the following features. The computingsystem is configured to generate the plurality of model waveforms for aplurality of assumed thicknesses based on one or more of (i) areflection of the acoustic signal, (ii) a radiation pattern of theacoustic transmitter, and (iii) a curvature of the well casing. Thecomputing system is configured to determine the thickness of the wellcasing in real time during drilling operations or wireline loggingoperations.

Other implementations are within the scope of the following claims.

1. A method comprising: accessing a measured waveform associated with anacoustic signal returned via a well casing based on operating anacoustic transmitter and an acoustic receiver within a wellborecomprising the well casing; comparing the measured waveform to a modelwaveform, wherein the model waveform corresponds to an estimatedimpedance of a medium surrounding an exterior portion of the wellcasing, and the model waveform corresponds to a ray tracing of theacoustic signal that accounts for a radiation pattern of the acoustictransmitter and a curvature of the well casing; and determining, byoperation of data processing apparatus, an impedance of the mediumsurrounding the exterior portion of the well casing based on results ofcomparing the measured waveform to the model waveform.
 2. The method ofclaim 1, further comprising: decomposing the acoustic signal emittedfrom the acoustic transmitter into a plurality of rays; calculatingcharacteristics of each of the plurality of rays based on the radiationpattern of the acoustic transmitter and the curvature of the wellcasing; determining a subset of the plurality of rays that are returnedvia the well casing and detected by the acoustic receiver; and combiningthe characteristics of the subset of the plurality of rays to generatethe model waveform.
 3. The method of claim 1, wherein: comparing themeasured waveform to the model waveform comprises comparing differencesbetween the measured waveform and the model waveform; and determiningthe impedance of the medium comprises determining optimal fitting valuesfor the impedance of the medium based on results of comparing thedifferences between the measured waveform and the model waveform.
 4. Themethod of claim 1, wherein comparing the measured waveform to the modelwaveform comprises applying an inversion technique to compare themeasured waveform and the model waveform.
 5. The method of claim 4,wherein the inversion technique comprises a one-dimensional grid search.6. The method of claim 4, wherein the inversion technique comprises ageneralized linear inversion.
 7. The method of claim 4, wherein theinversion technique comprises a non-linear inversion.
 8. The method ofclaim 1, wherein determining the impedance of the medium comprisesdetermining the impedance of the medium in real time during drillingoperations or wireline logging operations.
 9. A non-transitorycomputer-readable medium encoded with instructions that, when executedby data processing apparatus, cause the data processing apparatus toperform operations comprising: accessing a measured waveform associatedwith an acoustic signal returned via a well casing based on operating anacoustic transmitter and an acoustic receiver within a wellborecomprising the well casing; comparing the measured waveform to a modelwaveform, wherein the model waveform corresponds to an estimatedimpedance of a medium surrounding an exterior portion of the wellcasing, and the model waveform corresponds to a ray tracing of theacoustic signal that accounts for a radiation pattern of the acoustictransmitter and a curvature of the well casing; and determining animpedance of the medium surrounding the exterior portion of the wellcasing based on results of comparing the measured waveform to the modelwaveform.
 10. The non-transitory computer-readable medium of claim 9,wherein the operations further comprise: decomposing the acoustic signalemitted from the acoustic transmitter into a plurality of rays;calculating characteristics of each of the plurality of rays based onthe radiation pattern of the acoustic transmitter and the curvature ofthe well casing; determining a subset of the plurality of rays that arereturned via the well casing and detected by the acoustic receiver; andcombining the characteristics of the subset of the plurality of rays togenerate the model waveform.
 11. The non-transitory computer-readablemedium of claim 9, wherein: comparing the measured waveform to the modelwaveform comprises comparing differences between the measured waveformand the model waveform; and determining the impedance of the mediumcomprises determining optimal fitting values for the impedance of themedium based on results of comparing the differences between themeasured waveform and the model waveform.
 12. The non-transitorycomputer-readable medium of claim 9, wherein comparing the measuredwaveform to the model waveform comprises applying an inversion techniqueto compare the measured waveform and the model waveform.
 13. Thenon-transitory computer-readable medium of claim 12, wherein theinversion technique comprises a one-dimensional grid search.
 14. Thenon-transitory computer-readable medium of claim 12, wherein theinversion technique comprises a generalized linear inversion.
 15. Thenon-transitory computer-readable medium of claim 12, wherein theinversion technique comprises a non-linear inversion.
 16. Thenon-transitory computer-readable medium of claim 9, wherein determiningthe impedance of the medium comprises determining the impedance of themedium in real time during drilling operations or wireline loggingoperations.
 17. A system comprising: an acoustic transmitter-receiverpair to be disposed within a wellbore comprising a well casing; and acomputing system coupled with the acoustic transmitter-receiver pair,the computing system is configured to: access a measured waveformassociated with an acoustic signal returned via the well casing based onoperating an acoustic transmitter and an acoustic receiver within aninterior portion of the well casing; compare the measured waveform to amodel waveform, wherein the model waveform corresponds to an estimatedimpedance of a medium surrounding an exterior portion of the wellcasing, and the model waveform corresponds to a ray tracing of theacoustic signal that accounts for a radiation pattern of the acoustictransmitter and a curvature of the well casing; and determine animpedance of the medium surrounding the exterior portion of the wellcasing based on results of comparing the measured waveform to the modelwaveform.
 18. The system of claim 17, wherein the computing system isconfigured to: decompose the acoustic signal emitted from the acoustictransmitter into a plurality of rays; calculate characteristics of eachof the plurality of rays based on the radiation pattern of the acoustictransmitter and the curvature of the well casing; determine a subset ofthe plurality of rays that are returned via the well casing and detectedby the acoustic receiver; and combine the characteristics of the subsetof the plurality of rays to generate the model waveform.
 19. The systemof claim 17, wherein: the computing system is configured to compare themeasured waveform to the model waveform comprises the computing systemis configured to compare differences between the measured waveform andthe model waveform; and the computing system is configured to determinethe impedance of the medium comprises the computing system is configuredto determine optimal fitting values for the impedance of the mediumbased on results of comparing the differences between the measuredwaveform and the model waveform.
 20. The system of claim 17, wherein thecomputing system is configured to compare the measured waveform to themodel waveform comprises the computing system is configured to apply aninversion technique to compare the measured waveform and the modelwaveform. 21.-24. (canceled)